CN116794987A - Heterogeneous multi-agent system consistency control method based on event trigger control - Google Patents
Heterogeneous multi-agent system consistency control method based on event trigger control Download PDFInfo
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Abstract
The invention discloses a heterogeneous multi-agent system consistency control method based on event trigger control, wherein the heterogeneous multi-agent system comprises m first-order multi-agents and N-m second-order multi-agents, and the communication is carried out through a weighted undirected network; firstly, when the heterogeneous multi-agent system converges to be consistent, the positions of the agents converge to the average value of the positions, the speed converges to 0, and the position convergence average value is defined; and then the consistency problem of the heterogeneous multi-agent system is converted into a stability problem, and the consistency control of the heterogeneous multi-agent system is realized through the sectional control input rate and the event trigger control. The invention combines the event trigger control of the combined measurement method and inherits the consistency of the first-order second-order heterogeneous multi-agent system. And communication resource loss is reduced. The condition of the matrix Q is that its minimum singular value is greater than 0 to reduce the conservation of the event triggering condition.
Description
Technical Field
The invention belongs to the technical field of distributed control, relates to a multi-agent system consistency control method, and in particular relates to a heterogeneous multi-agent system consistency control method based on event trigger control.
Background
Distributed coordination control of multi-agent systems has received a great deal of attention due to their wide application in formation control, cluster control, and bee congestion control. Centralized control requires that each node has a network communication with a good connection with the central controller, as compared with distributed control, but in practical application, the centralized control often has difficulty in well achieving a predetermined control effect due to the influence of communication delay and other factors, and the probability of failure of the centralized control is higher than that of the distributed control due to possible single-point failure. The distributed control reduces the influence of communication time lag between the central controller and each node in the centralized control, so that the system can adapt to the dynamically-changed operation environment, the dependence on global communication is reduced, and the fault tolerance and the robustness of the system are improved.
The consistency problem is one of the most basic distributed coordination control problems, is the crossing field of control system theory and graph theory, and is a process which relates to a series of intelligent agents to achieve a common target through information interaction and sharing. Consistency refers to the fact that the states of the intelligent agent system eventually approach the same value at a certain moment in time, and the states can be the motion gesture of satellites, the action direction of shoal or shoal, data fusion or the filtering value of a distributed sensor.
At present, research on consistency problems is focused on collaborative consistency control of a first-order system, a second-order system, a high-order system and a heterogeneous system. "Distributed event-triggered control of multi-agent systems with combinational measurements" proposes an event-triggered control of a combined measurement method, which, unlike the previous event-triggered control, the agents trigger only at their own event time without regard to the trigger moment of the neighbors, which in practice reduces the traffic and reduces the frequency of controller updates. This approach provides one approach to feasibility but does not consider a first-order, second-order heterogeneous multi-agent system. "Distributed event-triggered consensus control for leaderless heterogeneous multiagent systems" uses a distributed event-triggered control method to control the first-order second-order heterogeneous multi-agent system to achieve an average consistent position, converge the speed to 0, and exclude the zeno behavior of the system, but the scheme does not consider event-triggered control of a combined measurement method, and cannot better reduce the energy consumption of control input update.
Disclosure of Invention
In order to solve the technical problems, the invention provides a heterogeneous multi-agent system consistency control method based on event trigger control.
The technical scheme adopted by the method is as follows: the heterogeneous multi-agent system consistency control method based on event trigger control comprises the steps that the heterogeneous multi-agent system comprises m first-order multi-agents and N-m second-order multi-agents, and communication is carried out through a weighted undirected network;
firstly, when the heterogeneous multi-agent system converges to be consistent, the positions of the agents converge to the average value of the positions, the speed converges to 0, and the position convergence average value is defined; and then the consistency problem of the heterogeneous multi-agent system is converted into a stability problem, and the consistency control of the heterogeneous multi-agent system is realized through the sectional control input rate and the event trigger control.
The invention also provides a heterogeneous multi-agent system consistency control system based on event trigger control, which comprises:
one or more processors;
and the storage device is used for storing one or more programs, and when the one or more programs are executed by the one or more processors, the one or more processors realize the heterogeneous multi-agent system consistency control method based on the event trigger control.
The invention also provides a storage medium which stores a program, and when the program is executed by a processor, the heterogeneous multi-agent system consistency control method based on event trigger control is realized.
Compared with the prior art, the invention has the advantages that:
(1) The event triggering control of the combined measurement method is combined, the system consistency of the first-order second-order heterogeneous multi-agent is inherited, and the communication resource loss is reduced.
(2) The condition of the matrix Q is that its minimum singular value is greater than 0 to reduce the conservation of the event triggering condition.
Drawings
The following examples, as well as specific embodiments, are used to further illustrate the technical solutions herein. In addition, in the course of describing the technical solutions, some drawings are also used. Other figures and the intent of the present invention can be derived from these figures without inventive effort for a person skilled in the art.
FIG. 1 is a diagram of a multi-intelligent system topology according to an embodiment of the present invention;
FIG. 2 is a position status update diagram of an embodiment of the present invention;
FIG. 3 is a speed state update diagram of an embodiment of the present invention;
FIG. 4 is a control input update diagram of an embodiment of the present invention;
fig. 5 is a diagram of heterogeneous multi-agent triggering times according to an embodiment of the present invention.
Detailed Description
In order to facilitate the understanding and practice of the invention, those of ordinary skill in the art will now make further details with reference to the drawings and examples, it being understood that the examples described herein are for the purpose of illustration and explanation only and are not intended to limit the invention thereto.
The invention provides a heterogeneous multi-agent system consistency control method based on event trigger control, wherein the heterogeneous multi-agent system comprises m first-order multi-agents and N-m second-order multi-agents, and the communication is carried out through a weighted undirected network;
firstly, when the heterogeneous multi-agent system converges to be consistent, the positions of the agents converge to the average value of the positions, the speed converges to 0, and the position convergence average value is defined; and then the consistency problem of the heterogeneous multi-agent system is converted into a stability problem, and the consistency control of the heterogeneous multi-agent system is realized through the sectional control input rate and the event trigger control.
In one embodiment, the topology map of the weighted undirected network is defined as g= { V, epsilon, a }, v= { V 1 ,V 2 ,...,V N Represents a node set, V i I is more than or equal to 1 and less than or equal to N, which represent an agent with the number i;representing a set of edges; a= [ a ] ij ]∈R N×N Representing a weighted adjacency matrix, a if there is an information link between agent i and agent j ij =1, otherwise a ij =0; defining D as a degree matrix, and a laplace matrix l=d-a;
when i=1, 2, once again, m, defining the kinetic equation of the first-order agent asWhen i=m+1, m+2, once again, N, defining the kinetic equation of the second order agent as +.>Wherein t represents time; each agent stores own state information, and the position state value of the ith agent at the moment t is defined as x i (t), the velocity state value of the last N-m intelligent agents at the time t is v i (t)；
Defining a consistency protocol:
wherein x is i (t)、x j (t) the position state information of the ith and jth agents at the time t respectively; v i (t)、v j (t) respectively representing the speed state information of the ith and jth intelligent agents at the moment t; i m Representing the first m intelligent agents in N intelligent agents, namely a first-order intelligent agent set, I N-m Representing N-m intelligent agents after N intelligent agents are among the N intelligent agents, namely a second-order intelligent agent set; b ij The weight value of the weighted adjacent matrix corresponding to the speed topology of the second-order intelligent agent is represented; alpha, beta is that the feedback gain of the system satisfies alpha>0,β>0；L A ＝[a ij ] N×N ,L B ＝[b ij ] (N-m)×(N-m) Is a position diagram G p And velocity graph G v Is j epsilon N i Is a neighbor set of agent i;
definition of kth of agent iThe triggering time of each event isRespectively representing that the intelligent agents i and j are in +.>The position sampling state and the speed sampling state at the moment are carried into the formula (3) to obtain:
substituting formula (4) into formulas (1) and (2) to obtain:
the combined measurement position and the combined measurement speed of the intelligent agent i at the adjacent intelligent agent j are as follows:
substituting formula (6) into formula (5) to obtain:
defining a sampling data measurement error as:
wherein e f,x (t)＝(e 1,x (t),e 1,x (t),...,e m,x (t)) T ,e s,x (t)＝(e m+1,x (t),e m+2,x (t),...,e N,x (t)) T ,e s,v (t)＝(e m+1,v (t),e m+2,v (t),...,e N,v (t)) T ，x f (t)＝(x 1 (t),x 2 (t),...,x m (t)) T ,x s (t)＝(x m+1 (t),x m+2 (t),...,x N (t)) T ,v s (t)＝(v m+1 (t),v m+2 (t),...,v N (t)) T ；
Bringing formula (8) into formula (7) to obtain:
formula (9) is further written as:
order theThe system rewrites into a matrix form:
wherein the method comprises the steps ofL 11 、L 12 、L 21 、L 22 Represents L A Block matrix, L 11 ∈R m*m ，L 12 ∈R m*(N-m) ，L 21 ∈R (N-m)*m ，L 22 ∈R (N-m)*(N-m) 。
The dynamics equation of the system knows that when the first-order second-order heterogeneous multi-agent system converges to be consistent, the positions of the agents converge to the average value of the positions, and the speed converges to 0; the position convergence average is thus defined as:
defining a column vector +.>
Error signal of systemThe error system is:
when (when)When (I)>Equivalent to->
The problem of consistency of the heterogeneous multi-agent system (11) translates into a problem of stability of the research system (12).
And (3) marking epsilon (t) as epsilon, and constructing a Lyapunov function:
V(t)＝ε T Pε (13)；
wherein P is a positive definite symmetric matrix;
deriving V (t) to obtain:
wherein P is a positive definite symmetric matrix defining a matrix q=g T P+PG-PK, matrix P exists such that svd min (Q)>0；svd min (Q) represents the singular value of matrix Q minimum;
definition lambda max (P) is the maximum eigenvalue of the matrix P, and I K I is the spectrum norm of the matrix K; then equation (14) is further written as:
force e i Satisfy the following requirementsWhen sigma is i E (0, 1), a negative +.> Over time, upon a change in condition (16), agent i will event trigger; meanwhile, the measurement error of the intelligent agent i is set to 0, and the control law is updated according to the formula (4), otherwise, the control rate is unchanged;
according to Lamulle invariant principle, defining Lamulle invariant setRepresentation->
The method further comprises the following steps:
i.e. the problem of consistency of heterogeneous multi-agent systems is solved.
The systems (1) and (2) control the input rate (4) and the event trigger function (16) in segments under the undirected communication topology G, and for any initial condition, at least one agent r E V exists, the time interval of which isStrictly positive, lower bound τ r >0。
The proving process is as follows: definition r=argmax i ||ε i And consider ||e i The method is characterized in that the I is less than or equal to E, which is true for all intelligent objects i, and can be obtained:definition τ r Is->Increase from 0 to->Time τ of (2) * Is->Increase from 0 to->From the above inequality, τ r Ratio τ * And is large.
Definition of the definitionAvailable->Suppose θ (t, θ) 0 ) Is an equationAnd θ (0, θ) 0 )＝θ 0 Thus phi is less than or equal to theta (t, theta) 0 ) The minimum time interval can be obtained by calculating the time of this differential equation: />
Assuming that the system is started at the time of the first event trigger, θ 0 Otherwise the system will evolve continuously, at least for one agent its absolute measurement error will increase without resetting.
Defining τ is a solution to equation (17), and can be obtainedOrder theThe minimum time interval between any two agentsObviously τ * >0, it is demonstrated that the event does not trigger indefinitely, thus excluding the gano action.
The invention is explained in further detail by the following experiments.
The present experiment considered the following system:the topology of which is shown in figure 1.
Wherein agents 1 and 2 are first order integral agents and agents 3 and 4 are second order integral agents. Laplacian matrix L of a position topology A And L B The method comprises the following steps of:the feedback gain α=1, β=1, and the initial state of the system position is x= (2, -1, -2, 3) T The initial state of the speed is v= (-1, 1) T The parameter delta is set to delta 1 ＝δ 2 ＝δ 3 ＝δ 4 ＝δ 5 ＝δ 6 =0.9. Fig. 2 and 3 show that the position and velocity of the agent are consistent, respectively. FIG. 4 shows the control inputs of the system, and it can be seen from FIG. 4 that after the agent reaches the consensus targetIs 0. FIG. 5 shows the number of triggers per agent, time stamps [0s,10s ] by simulation]The system is divided into 1000 intervals, each interval h=0.01 s, the triggering times of each intelligent agent are 47 times, 81 times and 81 times respectively, if the system is not triggered by an event, the control update needs to be updated at least 1000 times, and as can be seen from fig. 5, the input update times are effectively reduced.
The invention realizes the consistency of first-order second-order heterogeneous multi-agent of the event trigger control of the combined measurement method, and the event trigger control of the combined measurement method reduces the loss of communication resources, and has the following key points:
1. feedback gain alpha, beta, designed constant sigma i Are controlled within a reasonable range.
2. The intelligent agents are triggered only at their own event time without considering the triggering time of neighbors, so that the communication frequency and the energy consumption are reduced, and the 'Zhinon' phenomenon is avoided.
3. The first-order second-order heterogeneous multi-intelligent system model is discussed, and the method is more suitable for some situations in practice.
It should be understood that the foregoing description of the preferred embodiments is not intended to limit the scope of the invention, but rather to limit the scope of the claims, and that those skilled in the art can make substitutions or modifications without departing from the scope of the invention as set forth in the appended claims.
Claims (5)
1. A heterogeneous multi-agent system consistency control method based on event trigger control is characterized in that: the heterogeneous multi-intelligent system comprises m first-order multi-intelligent agents and N-m second-order multi-intelligent agents, and the communication is carried out through a weighted undirected network;
firstly, when the heterogeneous multi-agent system converges to be consistent, the positions of the agents converge to the average value of the positions, the speed converges to 0, and the position convergence average value is defined; and then the consistency problem of the heterogeneous multi-agent system is converted into a stability problem, and the consistency control of the heterogeneous multi-agent system is realized through the sectional control input rate and the event trigger control.
2. The heterogeneous multi-agent system consistency control method based on event trigger control according to claim 1, wherein: the topology of the weighted undirected network is defined as g= { V, epsilon, a }, v= { V 1 ,V 2 ,...,V N Represents a node set, V i I is more than or equal to 1 and less than or equal to N, which represent an agent with the number i;representing a set of edges; a= [ a ] ij ]∈R N×N Representing a weighted adjacency matrix, a if there is an information link between agent i and agent j ij =1, otherwise a ij =0; defining D as a degree matrix, and a laplace matrix l=d-a;
when i=1, 2, once again, m, defining the kinetic equation of the first-order agent as(1) The method comprises the steps of carrying out a first treatment on the surface of the When i=m+1, m+2, once again, N, defining the kinetic equation of the second order agent as +.>(2) The method comprises the steps of carrying out a first treatment on the surface of the Wherein t represents time; each agent stores own state information, and the position state value of the ith agent at the moment t is defined as x i (t), the velocity state value of the last N-m intelligent agents at the time t is v i (t)；
Defining a consistency protocol:
wherein x is i (t)、x j (t) the position state information of the ith and jth agents at the time t respectively; v i (t)、v j (t) represents the time t of the ith and jth agentSpeed status information; i m Representing the first m intelligent agents in N intelligent agents, namely a first-order intelligent agent set, I N-m Representing N-m intelligent agents after N intelligent agents are among the N intelligent agents, namely a second-order intelligent agent set; b ij The weight value of the weighted adjacent matrix corresponding to the speed topology of the second-order intelligent agent is represented; alpha, beta is that the feedback gain of the system satisfies alpha>0,β>0；L A ＝[a ij ] N×N ,L B ＝[b ij ] (N-m)×(N-m) Is a position diagram G p And velocity graph G v Is j epsilon N i Is a neighbor set of agent i;
defining the kth event trigger time of the intelligent body i asRespectively representing that the intelligent agents i and j are in +.>The position sampling state and the speed sampling state at the moment are carried into the formula (3) to obtain:
substituting formula (4) into formulas (1) and (2) to obtain:
the combined measurement position and the combined measurement speed of the intelligent agent i at the adjacent intelligent agent j are as follows:
substituting formula (6) into formula (5) to obtain:
defining a sampling data measurement error as:
wherein e f,x (t)＝(e 1,x (t),e 1,x (t),...,e m,x (t)) T ,e s,x (t)＝(e m+1,x (t),e m+2,x (t),...,e N,x (t)) T ,e s,v (t)＝(e m+1,v (t),e m+2,v (t),...,e N,v (t)) T ，x f (t)＝(x 1 (t),x 2 (t),...,x m (t)) T ,x s (t)＝(x m+1 (t),x m+2 (t),...,x N (t)) T ,v s (t)＝(v m+1 (t),v m+2 (t),...,v N (t)) T ；
Bringing formula (8) into formula (7) to obtain:
formula (9) is further written as:
order theThe system rewrites into a matrix form:
wherein the method comprises the steps ofL 11 、L 12 、L 21 、L 22 Represents L A Block matrix, L 11 ∈R m*m ，L 12 ∈R m*(N-m) ，L 21 ∈R (N-m)*m ，L 22 ∈R (N-m)*(N-m) ；
The dynamics equation of the system knows that when the first-order second-order heterogeneous multi-agent system converges to be consistent, the positions of the agents converge to the average value of the positions, and the speed converges to 0; the position convergence average is thus defined as:defining a column vector +.>
Error signal of systemThe error system is:
when (when)When (I)>Equivalent to-> The problem of consistency of the heterogeneous multi-agent system (11) translates into a problem of stability of the research system (12).
3. The heterogeneous multi-agent system consistency control method based on event trigger control according to claim 2, wherein:
constructing a Lyapunov function:
V(t)＝ε T (t)Pε(t) (13)；
wherein P is a positive definite symmetric matrix, and epsilon (t) is epsilon;
deriving V (t) to obtain:
defining a matrix q=g T P+PG-PK, matrix P exists such that svd min (Q)>0；svd min (Q) represents the singular value of matrix Q minimum;
definition lambda max (P) is the maximum eigenvalue of the matrix P, and I K I is the spectrum norm of the matrix K; then equation (14) is further written as:
force e i Satisfy the following requirementsWhen sigma is i E (0, 1), a negative +.> Over time, upon a change in condition (16), agent i will event trigger; meanwhile, the measurement error of the intelligent agent i is set to 0, and the control law is updated according to the formula (4), otherwise, the control rate is unchanged;
according to Lamulle invariant principle, defining Lamulle invariant set Representation->
The method further comprises the following steps:
i.e. the problem of consistency of heterogeneous multi-agent systems is solved.
4. A heterogeneous multi-agent system consistency control system based on event-triggered control, comprising:
one or more processors;
storage means for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to implement the heterogeneous multi-agent system consistency control method based on event trigger control as claimed in any one of claims 1 to 3.
5. A storage medium storing a program, wherein the program, when executed by a processor, implements the heterogeneous multi-agent system consistency control method based on event trigger control as claimed in any one of claims 1 to 3.
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| CN117687345B (en) * | 2024-02-01 | 2024-05-14 | 北京中关村实验室 | Control method of multi-agent system and related products |
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